{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:6F3RJ4SM53HP3MGBG7QQX3MPVM","short_pith_number":"pith:6F3RJ4SM","canonical_record":{"source":{"id":"gr-qc/9809054","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"1998-09-17T14:15:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"92628b707a5d94f547945b0e84c54cfdd4614b5e8c26f07e1b54b95fd465682a","abstract_canon_sha256":"a98f70dbaf009fcb18aa14d834dcc633490d2bde6090abb52c98e651aaa1a296"},"schema_version":"1.0"},"canonical_sha256":"f17714f24ceecefdb0c137e10bed8fab34bd5405defb98f7c7bc7655b0b2379f","source":{"kind":"arxiv","id":"gr-qc/9809054","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9809054","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9809054v3","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9809054","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"6F3RJ4SM53HP","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6F3RJ4SM53HP3MGB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6F3RJ4SM","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:6F3RJ4SM53HP3MGBG7QQX3MPVM","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9809054","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"1998-09-17T14:15:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"92628b707a5d94f547945b0e84c54cfdd4614b5e8c26f07e1b54b95fd465682a","abstract_canon_sha256":"a98f70dbaf009fcb18aa14d834dcc633490d2bde6090abb52c98e651aaa1a296"},"schema_version":"1.0"},"canonical_sha256":"f17714f24ceecefdb0c137e10bed8fab34bd5405defb98f7c7bc7655b0b2379f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:47.624920Z","signature_b64":"wwMCOikBnG2sN3Ta7Gg8OhmsBmFww//ljExQr09DV23+m1+39VmsJKgn72+SslJ64/HQ/cj25HFjpkQROLGEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f17714f24ceecefdb0c137e10bed8fab34bd5405defb98f7c7bc7655b0b2379f","last_reissued_at":"2026-05-18T03:11:47.624144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:47.624144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9809054","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4+xb6CW6ga9l1Etg7Zsd0T2rolgNTANruqMdv763XHud4PHBGobghLtG7rRdnoPeAjclmqWc6wdXrbMdFpBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:28:53.589124Z"},"content_sha256":"5c480115f8bfb402104336018dc377a816b2ae37e48e98df6e1194ecb0848b83","schema_version":"1.0","event_id":"sha256:5c480115f8bfb402104336018dc377a816b2ae37e48e98df6e1194ecb0848b83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:6F3RJ4SM53HP3MGBG7QQX3MPVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the geometry of impulsive gravitational waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Roland Steinbauer","submitted_at":"1998-09-17T14:15:32Z","abstract_excerpt":"We describe impulsive gravitational pp-waves entirely in the distributional picture. Applying Colombeau's nonlinear framework of generalized functions we handle the formally ill-defined products of distributions which enter the geodesic as well as the geodesic deviation equation. Using a universal regularization procedure we explicitly derive regularization independent distributional limits. In the special case of impulsive plane waves we compare our results with the particle motion derived from the continuous form of the metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9809054","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kX+cibuKVxnPs5n3Bx+gFJG1GFasms1l73zRODwQAFioAloKSVf+y86eFCtBbmD/B/cI7yW22djJG5zEDHpUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:28:53.589489Z"},"content_sha256":"ad495fe0b0f9a3eabd03b9cd47551c0c8b0074b6bdbba380e8630c3e97d0e73d","schema_version":"1.0","event_id":"sha256:ad495fe0b0f9a3eabd03b9cd47551c0c8b0074b6bdbba380e8630c3e97d0e73d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM/bundle.json","state_url":"https://pith.science/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T10:28:53Z","links":{"resolver":"https://pith.science/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM","bundle":"https://pith.science/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM/bundle.json","state":"https://pith.science/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6F3RJ4SM53HP3MGBG7QQX3MPVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:6F3RJ4SM53HP3MGBG7QQX3MPVM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a98f70dbaf009fcb18aa14d834dcc633490d2bde6090abb52c98e651aaa1a296","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"1998-09-17T14:15:32Z","title_canon_sha256":"92628b707a5d94f547945b0e84c54cfdd4614b5e8c26f07e1b54b95fd465682a"},"schema_version":"1.0","source":{"id":"gr-qc/9809054","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9809054","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9809054v3","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9809054","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"6F3RJ4SM53HP","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6F3RJ4SM53HP3MGB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6F3RJ4SM","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:ad495fe0b0f9a3eabd03b9cd47551c0c8b0074b6bdbba380e8630c3e97d0e73d","target":"graph","created_at":"2026-05-18T03:11:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We describe impulsive gravitational pp-waves entirely in the distributional picture. Applying Colombeau's nonlinear framework of generalized functions we handle the formally ill-defined products of distributions which enter the geodesic as well as the geodesic deviation equation. Using a universal regularization procedure we explicitly derive regularization independent distributional limits. In the special case of impulsive plane waves we compare our results with the particle motion derived from the continuous form of the metric.","authors_text":"Roland Steinbauer","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"1998-09-17T14:15:32Z","title":"On the geometry of impulsive gravitational waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9809054","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5c480115f8bfb402104336018dc377a816b2ae37e48e98df6e1194ecb0848b83","target":"record","created_at":"2026-05-18T03:11:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a98f70dbaf009fcb18aa14d834dcc633490d2bde6090abb52c98e651aaa1a296","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"1998-09-17T14:15:32Z","title_canon_sha256":"92628b707a5d94f547945b0e84c54cfdd4614b5e8c26f07e1b54b95fd465682a"},"schema_version":"1.0","source":{"id":"gr-qc/9809054","kind":"arxiv","version":3}},"canonical_sha256":"f17714f24ceecefdb0c137e10bed8fab34bd5405defb98f7c7bc7655b0b2379f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f17714f24ceecefdb0c137e10bed8fab34bd5405defb98f7c7bc7655b0b2379f","first_computed_at":"2026-05-18T03:11:47.624144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:47.624144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wwMCOikBnG2sN3Ta7Gg8OhmsBmFww//ljExQr09DV23+m1+39VmsJKgn72+SslJ64/HQ/cj25HFjpkQROLGEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:47.624920Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9809054","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c480115f8bfb402104336018dc377a816b2ae37e48e98df6e1194ecb0848b83","sha256:ad495fe0b0f9a3eabd03b9cd47551c0c8b0074b6bdbba380e8630c3e97d0e73d"],"state_sha256":"e327f9fbfa8c68b2a3a462d412de71381ff88c557a50e9e5869fb931597a1c55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9jdAbzUQ2W9BHPVB9fIq/tLqCdlnWOtAsukeF7ZVZeV/KZpbQQu6Mpu4+YB+SNGhoX+yqeSlvs9jzlWpySbCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:28:53.591452Z","bundle_sha256":"ab13ce354b401f11602e2766a7cb012066bfdeaa4dc3f0d8284619a8447a6beb"}}